Binomial RV: many biased coins.

p - probability of heads in one toss. N - number of tosses.

E[X] = (N)(p) E[Y] = N - (N)(p) = N (1 - p)

Y seems to be just like X, except with probability (1 - p).

Conclusion: Y is a binomial RV with parameters N and (1 - p).

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Basic linear algebra uncovers and clarifies very important geometry and algebra.

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